Effects of nonlinearity on the atmospheric flow response to low-level heating in a uniform flow

Effects of nonlinearity on the stably stratified atmospheric response to prescribed low-level heating in a uniform flow are investigated through nondimensional numerical model experiments over a wide range of the nonlinearity factors of thermally induced finite-amplitude waves (0 ≤ μ ≤ 4). The heating function is assumed to be uniform in the vertical from the surface to a nondimensional height of 2 and to be bell shaped in the horizontal. As the nonlinearity factor becomes larger, the flow response is quite different from the linear response due to the larger nonlinear advective effect. A strong updraft cell gradually appears on the downstream side with an increasing nonlinearity factor. In the highly nonlinear regime (μ ≳ 2.2), alternating weaker downdraft and updraft cells behind the leading updraft cell are observed on the downstream side. These alternating cells experience periodic cycles with the processes of linear and nonlinear advection, intensification, weakening, formation, disappearing, and merging to the leading updraft cell. These processes are connected with the oscillatory behavior of the perturbation horizontal velocity through the mass continuity equation for the hydrostatic, incompressible flow. In the highly nonlinear regime, there exists the secondary maximum of the perturbation horizontal velocity at the surface, which during its downstream advection intensifies, causes the primary maximum of the perturbation horizontal velocity to diminish, and becomes a new primary maximum for an oscillation period. It is suggested that the repeated formation of the secondary maximum of the perturbation horizontal velocity and its becoming the primary maximum are responsible for the oscillatory processes and the steadiness of the maximum perturbation averaged for an oscillation period. As the nonlinearity factor increases, the oscillation period decreases.